Fourth Hankel determinant for some subclasses of analytic functions

In the thesis, the fourth Hankel determinant for a subclass of starlike functions related to modified Sigmoid functions is discussed. Firstly, a coefficient estimation for the functions of this class has been made and then the upper bound for the fourth Hankel determinant has been determined. First of all, the basic definitions and theorems of complex functions theory are given. Then, univalent functions, its some important subclasses, some important subclasses in the unit disc of univalent functions and positive real functions classes have been introduced. Also some theorems about these classes have been stated. Subordination principles and their features have been explained, and then Hankel matrice has been defined. After that, Sigmoid function and its properties are mentioned and a subclass is defined for starlike functions related to Sigmoid functions and some coefficient estimations are obtained for this class. Finally, with these coefficients, an upper bound of the fourth Hankel determinant is obtained.